A boundary element based solution of an inverse elasticity problem by conjugate gradient and regularization method

A boundary element solution to an inverse elasticity problem by utilizing conjugate gradient method is presented for estimating the residual or contact stresses on a body from the measurements of displacement at discrete locations either internal to the domain or on part of the boundary which already has traction specified. The comparisons of the present method and commonly used regularization method are discussed systematically. The advantages and disadvantages in applying the large matrix (LM) and small matrix (SM) formulations are also examined. The present work is the first to the authors' knowledge to do above studies. Finally the effects of the measurement errors to the inverse solutions are discussed. A statistical analysis which leads to a 99% confidence bound will also be considered.